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Find the curvature of r(t) = (t, t², t³) at the point (1, 1, 1).

Find the curvature of r(t) = (t, t², t³) at the point (1, 1, 1).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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19. r(t) 20. r(t) = (1, 11², 1²) po brit 319MAXE 21-23 Use Theorem 10 to find the curvature. = 21. r(t) = t³j + t²k are many smele out bat 22. r(t) = ti + t²j+e¹k 23. r(t) = √√6t² i + 2t j + 2t³ k 24. Find the curvature of r(t) = (t², In t, t ln t ) at the point (1, 0, 0). 25. Find the curvature of r(t) = (t, t², t³) at the point (1, 1, 1). 26. Graph the curve with parametric equations x = cost, y = sin t, z = sin 5t and find the curvature at the point (1, 0, 0). 27-29 Use Formula 11 to find the curvature. 27. y=x4 28. y = tan x 30. y = ln x 32. 30-31 At what point does the curve have maximum curvature? What happens to the curvature as x→∞? E Dan xilad sal words & Susp because 10 Sigginza he ouela guilt T'orthogonal, to It Now 30R20 15 16 29. y = xe 31. y = et gunsinoed
Transcribed Image Text:19. r(t) 20. r(t) = (1, 11², 1²) po brit 319MAXE 21-23 Use Theorem 10 to find the curvature. = 21. r(t) = t³j + t²k are many smele out bat 22. r(t) = ti + t²j+e¹k 23. r(t) = √√6t² i + 2t j + 2t³ k 24. Find the curvature of r(t) = (t², In t, t ln t ) at the point (1, 0, 0). 25. Find the curvature of r(t) = (t, t², t³) at the point (1, 1, 1). 26. Graph the curve with parametric equations x = cost, y = sin t, z = sin 5t and find the curvature at the point (1, 0, 0). 27-29 Use Formula 11 to find the curvature. 27. y=x4 28. y = tan x 30. y = ln x 32. 30-31 At what point does the curve have maximum curvature? What happens to the curvature as x→∞? E Dan xilad sal words & Susp because 10 Sigginza he ouela guilt T'orthogonal, to It Now 30R20 15 16 29. y = xe 31. y = et gunsinoed
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